Interestingly, this probability can be bounded by reconsidering the statistics of detector counts in an auto-correlation measurement. This measurement, which is known to be valuable for witnessing various forms of non-classicality, including the negativity of the P-distribution and quantum non Gaussianity [1]}, [2]}, is here shown to enable the detection of the negativity of the Wigner representation [3]}, the strongest form of non-classicality. Considering a measure of Wigner negativity introduced in [4]}, we show that it is non-increasing under Gaussian operations and relate it to results observed in an auto-correlation measurement. This suggests a systematic way to benchmark the quality and quantify the efficiency of single-photon sources, and to witness and quantify their quantum nature. To help motivate benchmarking single photon sources by the probability that the source actually produces exactly a single photon, we provide a detailed analysis which includes a simple statistical tool to account for finite size effects without assuming that identical states were produced in all rounds of the experiment. We show how to include imperfections in the measurements apparatus and how to remove the detector efficiencies from the analysis to facilitate the use of the proposed benchmark. An experimental demonstration is presented, illustrating the quality of heralded single photon sources based on spontaneous parametric down-conversion.
